This paper investigates the channel diversity problem in high frequency (HF) communication systems. Due to the limited HF spectrum resources, a HF communication system with shared channels is considered, where each user equipment (UE) has individual communication demand. In order to maximize the communication probability of the whole system, a matching-potential game framework is designed. In detail, the channel diversity problem is decomposed into two sub-problems. One is channel-transmitter matching problem, which can be formulated as a many-to-one matching game. The other is the transmitter allocation problem which decides the transmission object that each transmitter communicates with under channel-transmitter matching result, and this sub-problem can be modeled as a potential game. A multiple round stable matching algorithm (MRSMA) is proposed, which obtains a stable matching result for the first sub-problem, and a distributed BR-based transmitter allocation algorithm (DBRTAA) is designed to reach Nash Equilibrium (NE) of the second sub-problem. Simulation results verify the effectiveness and superiority of the proposed method.